Hydrodynamics and Strength of Tornado Superchargers

Abstract

The article considers tornado fans and the principle for tornado occurrence in a free zone of the fan and the suction of this tornado, dusty air with transported material, in the funnel. This type of fans is used in pneumatic conveying of cotton and tea harvesting machines. The use of such fans eliminates mechanical damage to the transported material. In this paper, the authors consider the blades, outlined in a logarithmic spiral, while determining the geometric parameters of the blades is based on the theory of differential geometry. This allows one to obtain expressions for the parameters of the Lame shell–scapula and the main radii of curvature. The initial equations of the stress–strain state of the blade are obtained on the basis of the Lagrange variational principle. Subsequently, the resulting system of partial differential equations using the method of integral relations of Dorodnitsyn is reduced to a system of ordinary differential equations. Since the system of equations obtained contains variable coefficients, a modified method of successive approximations developed by Professor V. A. Pukhliy and presented by him in the academic press is applied to the solution of the obtained system. To accelerate the convergence of the solution, the authors use the method of telescopic shift of the Lanczos power series, for which the authors apply the possibility of representing any Mac-Lauren-type power series through shifted Chebyshev polynomials in the interval [0, 1].